Question

Suppose you have a 70-cm solenoid having a cross-sectional area of 9 cm². This is wound with 900 turns of wire and carries a current of 3.4 A. Suppose that its core has a relative permeability of 400. What is the flux in the solenoid?

Answer 1

The magnetic field inside a solenoid

$$B=\mu n I=k\mu_0\frac{N}{L}I$$

$$B=400*4\pi*10^{-7}*\frac{900}{0.7}*3.4=2.196\:\rm T$$

The magnetic flux

$$\Phi=BA\\ =2.196*9*10^{-4}=2.0*10^{-3}\:\rm Wb$$